Detekcja zmiany dryfu w modelowaniu natężenia śmiertelności
Drift change detection in mortality rate models

Summary/Abstract: Nowadays the insurance industry is facing huge challenges related to longevi-ty risk, i.e. the risk that the trend of longevity growth significantly changes in the future. One of the crucial steps in dealing with it is identifying the change of the mortality rate drift observed in prospective life tables. The purpose of this article is to identify this change by casting the problem of quickest detection in the framework of optimal stopping theory. We construct generalized discrete-time Shiryaev’s-Roberts statistics and we use it in the analysis of Polish life tables from years 1990-2014. We model the logarithm of the mortal intensity by the Brownian motion that changes the zero drift into nonzero one at some random time. For this case we construct optimal stopping rule detecting substantial change of this drift. We also present calibration of above model using Central Statistical Office data and we carry out extensive statistical analysis showing huge potential of described statistics.

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